An algorithm for the rapid evaluation of special function transforms

Michael O'Neil, Franco Woolfe, Vladimir Rokhlin

Research output: Contribution to journalArticle

Abstract

We introduce a new class of fast algorithms for the application to arbitrary vectors of certain special function transforms. The scheme is applicable to a number of transforms, including the Fourier-Bessel transform, the non-equispaced Fourier transform, transforms associated with all classical orthogonal polynomials, etc.; it requires order O (n log (n)) operations to apply an n × n matrix to an arbitrary vector. The performance of the algorithm is illustrated by several numerical examples.

Original languageEnglish (US)
Pages (from-to)203-226
Number of pages24
JournalApplied and Computational Harmonic Analysis
Volume28
Issue number2
DOIs
StatePublished - Mar 2010

Fingerprint

Special Functions
Transform
Evaluation
Fourier transforms
Polynomials
Classical Orthogonal Polynomials
Friedrich Wilhelm Bessel
Arbitrary
Fast Algorithm
Fourier transform
Numerical Examples

Keywords

  • Algorithm
  • Fast
  • Fourier-Bessel
  • Matrix
  • Special functions
  • Transform

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

An algorithm for the rapid evaluation of special function transforms. / O'Neil, Michael; Woolfe, Franco; Rokhlin, Vladimir.

In: Applied and Computational Harmonic Analysis, Vol. 28, No. 2, 03.2010, p. 203-226.

Research output: Contribution to journalArticle

O'Neil, Michael ; Woolfe, Franco ; Rokhlin, Vladimir. / An algorithm for the rapid evaluation of special function transforms. In: Applied and Computational Harmonic Analysis. 2010 ; Vol. 28, No. 2. pp. 203-226.
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